12) $$ \begin{aligned} x-8 y & =-22 \ -x+7 y & =19\end{aligned} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{aligned}
x - 8y &= -22 \quad \text{(1)} \
- x + 7y &= 19 \quad \text{(2)}
\end{aligned}
$$

**Step 1: Add the two equations to eliminate $$ x $$.**

$$
(x - 8y) + (-x + 7y) = -22 + 19
$$

Simplifying:

$$
- y = -3 \implies y = 3
$$

**Step 2: Substitute $$ y = 3 $$ into equation (1) to find $$ x $$.**

$$
x - 8(3) = -22 \
x - 24 = -22 \
x = -22 + 24 \
x = 2
$$

**Solution:**

$$
x = 2 \quad \text{and} \quad y = 3
$$
$$ x = 2 $$ and $$ y = 3 $$.

12) \( \begin{aligned} x-8 y & =-22 \\ -x+7 y & =19\end{aligned} \)